Generalizations of linear modelling in the biomedical sciences

Linear models have been very useful and popular in applied medical research. Linear model are simple to implement and they have the additional advantage of ease of interpretation. However, for more complex applied problems lesser known generalization of linear models are needed. Within the biomedical sciences there are many data sets of underlying complex processes that cannot be handled by means of linear regression. For example, individuals are measured across time or across different items inducing correlation. Or some bio-medical treatment may have one optimal value resulting in a nonlinear response. The aim of this thesis is to describe explanatory and predictive models that are generalizations of linear regression.

In longitudinal studies of psychiatry patients, the relationship between positive affect (such as happiness) and negative affect (such as depression and anxiety) is still controversial. We studied the question whether these two dimensions are independent or bipolar opposites and found that using a mixed effects model both of the dimensions are clearly related in obvious ways; they do not fully explain their opposite. Within urology, PCNL is the standard treatment option for kidney stones due to their high efficacy. However, the treatment may also have serious side-effects. Using a generalized additive model, we found that RIRS in certain scenarios can be as effective as PCNL, but much safer. Our findings make the better recommendations for improving health conditions of patients within the applied medical research and our approaches can be successfully used in bio-medical research.